Known steam cookers are often only useable to a limited extent in small baking ovens due to the shape of the steam cooker and particularly due to the mounting of the handles. Furthermore, with corresponding lids for steam cookers one can often observe the problems that such lids get unintentionally stuck by suction to the edge of the steam cooker or, however, e.g. in the case of an internal pressure inside the steam cooker that is higher than the external pressure of the surroundings, particularly during steam formation in the steam cooker, that an uncontrolled pressure equalization will take place so that an ordinary lid will be moving, clattering or even “dancing” on the steam cooker. Furthermore, during steam cooking attention should be paid to the problem that water vapor that is e.g. condensing on the lid or on the sides should flow back again into the steam cooker. Moreover, due to modern international cooking influences, there is often the desire to carry out multi-level steam cooking. Furthermore, in all modern appliances, particular attention is paid to the energy efficiency of the appliances and system.